Q.

A Straight line parallel to the line y=3x passes through Q(2,3) cuts the line 2x + 4y - 27 = 0 at P, Find the length of PQ.

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Detailed Solution

 Slope of the line y=3x is 3
 Slope of PQ is 3
 inclination of PQ is 60
If PQ = r then the coordiantes of P are
x1+rcosθ,y1+rsinθ=2+rcos600,3+rsin600=2+r2,3+3r2
Since P lies on the line 2x+4y27=0 then
22+r2+43+3r227=0r=231PQ=231   

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